论文标题
Lamperti的关系的多维版本和原始的Drift Therorem
A multi-dimensional version of Lamperti's relation and the Matsumoto-Yor opposite drift theorem
论文作者
论文摘要
一维布朗尼运动的经典结果表明，在其第一个打击时间为0的情况下，它具有3维贝塞尔桥的分布。通过在此结果中应用一定的时间变化，松本和YOR显示出与相反漂移之间的布朗运动之间的关系。相关的时间变化是出现在Lamperti的关系中的时间。 Sabot和Zeng表明，以相互作用漂移为条件的Brownian Motions家族在打击时间为0的载体，也具有独立的3维Bessel Bridges的分布。此外，这些打击时间的分布与对顶点增强跳跃过程的研究中出现的随机潜力有关。 本文的目的是通过将Lamperti-Type时间更改为以前的相互作用的Brownian Motions的家族来证明Matsumoto-Yor对面的多元版本。由于时间变化在不同坐标上以不同的速度进展，因此会出现困难。
A classic result on the 1-dimensional Brownian motion shows that conditionally on its first hitting time of 0, it has the distribution of a 3-dimensional Bessel bridge. By applying a certain time-change to this result, Matsumoto and Yor showed a theorem giving a relation between Brownian motions with opposite drifts. The relevant time change is the one appearing in Lamperti's relation. Sabot and Zeng showed that a family of Brownian motions with interacting drifts, conditioned on the vector of hitting times of 0, also has the distribution of independent 3-dimensional Bessel bridges. Moreover, the distribution of these hitting times is related to a random potential that appears in the study of the vertex-reinforced jump process. The aim of this paper is to prove a multivariate version of the Matsumoto-Yor opposite drift theorem, by applying a Lamperti-type time change to the previous family of interacting Brownian motions. Difficulties arise since the time change progresses at different speeds on different coordinates.
